# Geodesic measurements for short distances throughout US?

My ArcGIS experience has been limited to working on large-scale maps with planar projections. I'm moving to a project in which I want to calculate the distance between pro sports facilities throughout the U.S. and their city's respective downtown/central business district (both defined as geocoded points).

My primary interest is in relative distances, and my question is whether using a geographic coordinate system for US map points and using "Near" to calculate geodesic distances between stadia and downtowns is a sound approach to avoiding issues that would arise from calculating distance based on a projection of the US?

I am afraid that the answer is no: what you mean to do is correct but it will not work like this in ArcGIS with Near.

From the help, you can read that :

The distances calculated by this tool are in the unit of the coordinate system of the input features. If your input is in a geographic coordinate system and you want output distances to be measured in a linear unit (as opposed to decimal degrees), you must first project your input to a projected coordinate system using the Project tool. For best results, use an equidistant projection or a projection intended for your study area (UTM, for example)

in other words, if you use a geographic coordinate system, near will work as if it was a cartesian coordinate system.

You should instead use the Haversine approximation (see here ) or, better, the Vicenty's formula to find your solution (see @Michalis Avraam's answer)

• Thanks for this, everyone. The python script for the Haversine approximation looks like it should be more than sufficient. Appreciate the help! – Sean Mar 26 '14 at 19:52

There are some methods to calculate geodesic distances such as the haversine formula and Vincenty's formulae. These formulae are commonly used. The inverse Vincenty distance formula is the more accurate method to calculate the geodesic distance and is used in Google Maps, but it is slow.

• (1) I believe that Google Maps merely calculates the great circle distance (with a mean earth radius of 6371.009 km) instead of the geodesic distance. (2) It is an often-repeated myth that calculating the geodesic distance is slow. In fact the calculation takes about 2 us with compiled code on a present-day desktop computer -- maybe 5 times longer with "interpreted" code like JavaScript. In many applications, this counts as instantaneous. – cffk Aug 26 '15 at 15:16

No, if using the ArcGIS "Near" tool because, even if the coordinate system is geographic/geodetic, it does not calculate geodesic distances; it merely treats those geographic coordinates as though they were projected and thus gives results that cannot be compared across the US.

Yes, if you correctly calculate geodesic distances using geographic coordinates between points in or near downtown -- and you compare those with similar calculations made in completely different cities across the US -- you will have sound results. Doing it correctly means using spherical trigonometry (or some other geodetic technique).

Conversely, if you merely use plane coordinates -- taken from a single, national map projection -- and plane geometry for the same types of comparisons, you will not get sound results.

There are many questions that deal with such problems/methods on this site.